What is the timeout value difference in persistence and in a profile?

The default source address persistence timeout value is 180 seconds (3 minutes). This refers to how long the F5 will keep the persistence record entry in its persistence table. The F5 will purge the entry after if it has not received client traffic matching this persistence entry within 180 seconds

I assume the other timeout of 300 seconds you are referring applies to the TCP profile? This refers to the idle TCP timeout. The F5 will reap this connection from its connection table (sends a TCP reset back to the client) when the TCP connection idles out.